Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page ii
... examples . Babies ' Bourdon's Algebra - Including Sturm's and Horner's Theorems , and practical examples . Babies ' Legendre's Geometry and Trigonometry - Revised and adapted to the course of Mathematical Instruction in the United ...
... examples . Babies ' Bourdon's Algebra - Including Sturm's and Horner's Theorems , and practical examples . Babies ' Legendre's Geometry and Trigonometry - Revised and adapted to the course of Mathematical Instruction in the United ...
Page 26
... example , there will remain ( A. 5 ) , AC BC < AB ; - that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle ...
... example , there will remain ( A. 5 ) , AC BC < AB ; - that is , the difference between any two sides of a triangle is less than the third side . Scholium . In order that any three given lines may re- present the sides of a triangle ...
Page 74
... example , that this unit is contained 7 times in the angle ACB , and 4 times in the angle DOE ACB be divided into 7 angles , by the radii & c .; and DOE into 4 angles , by the radii Oz , each equal to the unit M. Then , suppose Cm , Cn ...
... example , that this unit is contained 7 times in the angle ACB , and 4 times in the angle DOE ACB be divided into 7 angles , by the radii & c .; and DOE into 4 angles , by the radii Oz , each equal to the unit M. Then , suppose Cm , Cn ...
Page 193
... example , that AE is to AI , as 15 is to 8 . Conceive AE to be which AI will contain 8 ; divided into 15 equal parts , of through the points of division let planes be passed parallel to ABCD . These planes will equal altitudes ; divide ...
... example , that AE is to AI , as 15 is to 8 . Conceive AE to be which AI will contain 8 ; divided into 15 equal parts , of through the points of division let planes be passed parallel to ABCD . These planes will equal altitudes ; divide ...
Page 252
... example , let them be to each other as 5 is to 48. Divide the circumference MNPQ into 48 equal parts , be- ginning at M ; MN will contain five of these parts . Join each point M N of division with the points A and B , by a quadrant ...
... example , let them be to each other as 5 is to 48. Divide the circumference MNPQ into 48 equal parts , be- ginning at M ; MN will contain five of these parts . Join each point M N of division with the points A and B , by a quadrant ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence